A-level Mathematics/AQA/Pure Core 1

Co-ordinate Geometry
- Equation of a line, y = mx + c
- Finding a line
  - two points
  - gradient, one points
  - etc.
- When are lines perpendicular or parallel?
Surds
- Simplification -
- Rationalising the Denominator.
Quadratics
- Diff b/w expression and equation
- Factorising
- Completing the square
  - Vertex of, line of symmetry of
- Formula
- Sketching
- Discriminant of
  - Implications made by discriminant value
Inequalities
- Three-part inequalities
- Quadratics
- Solution by sketch and completing square
Circles
- Circle Theorems
  - Tangents are perpen. to radii
  - Tangents from an external point are equal, etc.
  - MORE
- Co-ordinate Geometry Form of
- Circle from three points, finding tangents to a point
Other algebra
- Factor Theorem
- Remainder Theorem
- Simultanoues Eq.
  - Elimination
  - Substitution
- Curve Sketching
  - Intersections of curves as sol'n to sim. eq.
  - Translations of curves.
Diff'n
- IDEA: finding the gradient of the tangent to a curve
- As a limit
- function (f'(x), f(x)) and Liebniz notation (dy/dx)
- Diff'n polynomials
- Higher Derivatives
  - Stationary points
  - Maxima and Minima
- Increasing and decreasing functions
  - Practical Applications
Int'n
- Inverse process
- Net Area b/w curve and x-axis
  - Idea that below x-axis is NEGATIVE
- Diff b/w definite and indefinite int'n
- Area b/w curve and x-axis
- Are b/w two curves b/w two points
MASHUPS